Capstone Seminar in Advanced Mathematics

          Module 1: Foundations of Mathematical Reasoning

Section 1: Numbers and Operations  
- Lesson 1: Understanding Whole Numbers  
  Module 1, Section 1, Lesson 1: Understanding Whole Numbers  
- Lesson 2: Basic Arithmetic Operations  
  Module 1, Section 1, Lesson 2: Basic Arithmetic Operations  

Section 2: Fractions and Decimals  
- Lesson 1: Understanding Fractions  
  Module 1, Section 2, Lesson 1: Understanding Fractions  
- Lesson 2: Converting Between Fractions and Decimals  
  Module 1, Section 2, Lesson 2: Converting Between Fractions and Decimals  

Section 3: Ratios and Proportions  
- Lesson 1: Understanding Ratios  
  Module 1, Section 3, Lesson 1: Understanding Ratios  
- Lesson 2: Solving Proportions  
  Module 1, Section 3, Lesson 2: Solving Proportions  

Section 4: Basic Algebraic Concepts  
- Lesson 1: Introducing Variables  
  Module 1, Section 4, Lesson 1: Introducing Variables  
- Lesson 2: Forming and Simplifying Expressions  
  Module 1, Section 4, Lesson 2: Forming and Simplifying Expressions  

Section 5: Mathematical Problem-Solving Strategies  
- Lesson 1: Logical Reasoning in Math  
  Module 1, Section 5, Lesson 1: Logical Reasoning in Math  
- Lesson 2: Approaching Word Problems  
  Module 1, Section 5, Lesson 2: Approaching Word Problems  


Module 2: Fundamental Algebra

Section 1: Expressions and Equations  
- Lesson 1: Simplifying Algebraic Expressions  
  Module 2, Section 1, Lesson 1: Simplifying Algebraic Expressions  
- Lesson 2: Solving Simple Linear Equations  
  Module 2, Section 1, Lesson 2: Solving Simple Linear Equations  

Section 2: Linear Functions  
- Lesson 1: Understanding the Concept of a Function  
  Module 2, Section 2, Lesson 1: Understanding the Concept of a Function  
- Lesson 2: Graphing Linear Functions  
  Module 2, Section 2, Lesson 2: Graphing Linear Functions  

Section 3: Systems of Equations  
- Lesson 1: Introduction to Systems of Equations  
  Module 2, Section 3, Lesson 1: Introduction to Systems of Equations  
- Lesson 2: Solving Systems Graphically  
  Module 2, Section 3, Lesson 2: Solving Systems Graphically  

Section 4: Inequalities  
- Lesson 1: Understanding Inequalities  
  Module 2, Section 4, Lesson 1: Understanding Inequalities  
- Lesson 2: Solving Inequality Problems  
  Module 2, Section 4, Lesson 2: Solving Inequality Problems  

Section 5: Patterns and Sequences  
- Lesson 1: Recognizing Patterns  
  Module 2, Section 5, Lesson 1: Recognizing Patterns  
- Lesson 2: Introduction to Arithmetic Sequences  
  Module 2, Section 5, Lesson 2: Introduction to Arithmetic Sequences  


Module 3: Fundamental Geometry

Section 1: Basic Shapes and Properties  
- Lesson 1: Identifying Basic Geometric Shapes  
  Module 3, Section 1, Lesson 1: Identifying Basic Geometric Shapes  
- Lesson 2: Understanding Shape Properties  
  Module 3, Section 1, Lesson 2: Understanding Shape Properties  

Section 2: Perimeter, Area, and Volume  
- Lesson 1: Calculating Perimeter and Area  
  Module 3, Section 2, Lesson 1: Calculating Perimeter and Area  
- Lesson 2: Introduction to Volume Concepts  
  Module 3, Section 2, Lesson 2: Introduction to Volume Concepts  

Section 3: Angles and Lines  
- Lesson 1: Recognizing Different Types of Angles  
  Module 3, Section 3, Lesson 1: Recognizing Different Types of Angles  
- Lesson 2: Exploring Parallel and Perpendicular Lines  
  Module 3, Section 3, Lesson 2: Exploring Parallel and Perpendicular Lines  

Section 4: Coordinate Geometry  
- Lesson 1: Understanding the Coordinate Plane  
  Module 3, Section 4, Lesson 1: Understanding the Coordinate Plane  
- Lesson 2: Plotting Points on a Graph  
  Module 3, Section 4, Lesson 2: Plotting Points on a Graph  

Section 5: Transformation and Symmetry  
- Lesson 1: Exploring Lines of Symmetry  
  Module 3, Section 5, Lesson 1: Exploring Lines of Symmetry  
- Lesson 2: Basic Transformations (Translation, Rotation)  
  Module 3, Section 5, Lesson 2: Basic Transformations (Translation, Rotation)  


Module 4: Fundamental Data and Probability

Section 1: Data Collection and Analysis  
- Lesson 1: Methods of Collecting Data  
  Module 4, Section 1, Lesson 1: Methods of Collecting Data  
- Lesson 2: Analyzing Data Sets  
  Module 4, Section 1, Lesson 2: Analyzing Data Sets  

Section 2: Graphs and Charts  
- Lesson 1: Reading Bar Graphs and Line Graphs  
  Module 4, Section 2, Lesson 1: Reading Bar Graphs and Line Graphs  
- Lesson 2: Creating Basic Charts  
  Module 4, Section 2, Lesson 2: Creating Basic Charts  

Section 3: Statistical Measures  
- Lesson 1: Understanding Mean, Median, and Mode  
  Module 4, Section 3, Lesson 1: Understanding Mean, Median, and Mode  
- Lesson 2: Introduction to Range and Simple Variability  
  Module 4, Section 3, Lesson 2: Introduction to Range and Simple Variability  

Section 4: Basic Probability Concepts  
- Lesson 1: Fundamentals of Probability  
  Module 4, Section 4, Lesson 1: Fundamentals of Probability  
- Lesson 2: Simple Experiments and Chance  
  Module 4, Section 4, Lesson 2: Simple Experiments and Chance  

Section 5: Problem Solving with Data  
- Lesson 1: Interpreting Real-World Data  
  Module 4, Section 5, Lesson 1: Interpreting Real-World Data  
- Lesson 2: Simple Project-Based Data Investigations  
  Module 4, Section 5, Lesson 2: Simple Project-Based Data Investigations  


Module 5: Capstone Integration Project

Section 1: Research Methodologies in Mathematics  
- Lesson 1: Introduction to Mathematical Research  
  Module 5, Section 1, Lesson 1: Introduction to Mathematical Research  
- Lesson 2: Formulating a Research Question  
  Module 5, Section 1, Lesson 2: Formulating a Research Question  

Section 2: Project Planning and Design  
- Lesson 1: Outlining Your Project  
  Module 5, Section 2, Lesson 1: Outlining Your Project  
- Lesson 2: Setting Goals and Timelines  
  Module 5, Section 2, Lesson 2: Setting Goals and Timelines  

Section 3: Data Collection and Analysis for Projects  
- Lesson 1: Gathering Relevant Data  
  Module 5, Section 3, Lesson 1: Gathering Relevant Data  
- Lesson 2: Analyzing and Interpreting Project Data  
  Module 5, Section 3, Lesson 2: Analyzing and Interpreting Project Data  

Section 4: Presentation and Communication  
- Lesson 1: Preparing a Mathematical Presentation  
  Module 5, Section 4, Lesson 1: Preparing a Mathematical Presentation  
- Lesson 2: Effective Peer Review and Feedback  
  Module 5, Section 4, Lesson 2: Effective Peer Review and Feedback  

Section 5: Reflective Learning and Future Directions  
- Lesson 1: Reflecting on the Research Process  
  Module 5, Section 5, Lesson 1: Reflecting on the Research Process  
- Lesson 2: Applying Learnings to Future Mathematical Studies  
  Module 5, Section 5, Lesson 2: Applying Learnings to Future Mathematical Studies